Basic Math Examples

$(- 2 \sqrt{3} + 2) (\sqrt{3} - 5)$

Step 1

Expand $(- 2 \sqrt{3} + 2) (\sqrt{3} - 5)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$- 2 \sqrt{3} (\sqrt{3} - 5) + 2 (\sqrt{3} - 5)$

Step 1.2

Apply the distributive property.

$- 2 \sqrt{3} \sqrt{3} - 2 \sqrt{3} \cdot - 5 + 2 (\sqrt{3} - 5)$

Step 1.3

Apply the distributive property.

$- 2 \sqrt{3} \sqrt{3} - 2 \sqrt{3} \cdot - 5 + 2 \sqrt{3} + 2 \cdot - 5$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $- 2 \sqrt{3} \sqrt{3}$ .

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Step 2.1.1.1

Raise $\sqrt{3}$ to the power of $1$ .

$- 2 ({\sqrt{3}}^{1} \sqrt{3}) - 2 \sqrt{3} \cdot - 5 + 2 \sqrt{3} + 2 \cdot - 5$

Step 2.1.1.2

Raise $\sqrt{3}$ to the power of $1$ .

$- 2 ({\sqrt{3}}^{1} {\sqrt{3}}^{1}) - 2 \sqrt{3} \cdot - 5 + 2 \sqrt{3} + 2 \cdot - 5$

Step 2.1.1.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 2 {\sqrt{3}}^{1 + 1} - 2 \sqrt{3} \cdot - 5 + 2 \sqrt{3} + 2 \cdot - 5$

Step 2.1.1.4

Add $1$ and $1$ .

$- 2 {\sqrt{3}}^{2} - 2 \sqrt{3} \cdot - 5 + 2 \sqrt{3} + 2 \cdot - 5$

Step 2.1.2

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 2.1.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$- 2 {(3^{\frac{1}{2}})}^{2} - 2 \sqrt{3} \cdot - 5 + 2 \sqrt{3} + 2 \cdot - 5$

Step 2.1.2.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 2 \cdot 3^{\frac{1}{2} \cdot 2} - 2 \sqrt{3} \cdot - 5 + 2 \sqrt{3} + 2 \cdot - 5$

Step 2.1.2.3

Combine $\frac{1}{2}$ and $2$ .

$- 2 \cdot 3^{\frac{2}{2}} - 2 \sqrt{3} \cdot - 5 + 2 \sqrt{3} + 2 \cdot - 5$

Step 2.1.2.4

Cancel the common factor of $2$ .

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Step 2.1.2.4.1

Cancel the common factor.

$- 2 \cdot 3^{\frac{2}{2}} - 2 \sqrt{3} \cdot - 5 + 2 \sqrt{3} + 2 \cdot - 5$

Step 2.1.2.4.2

Rewrite the expression.

$- 2 \cdot 3^{1} - 2 \sqrt{3} \cdot - 5 + 2 \sqrt{3} + 2 \cdot - 5$

Step 2.1.2.5

Evaluate the exponent.

$- 2 \cdot 3 - 2 \sqrt{3} \cdot - 5 + 2 \sqrt{3} + 2 \cdot - 5$

Step 2.1.3

Multiply $- 2$ by $3$ .

$- 6 - 2 \sqrt{3} \cdot - 5 + 2 \sqrt{3} + 2 \cdot - 5$

Step 2.1.4

Multiply $- 5$ by $- 2$ .

$- 6 + 10 \sqrt{3} + 2 \sqrt{3} + 2 \cdot - 5$

Step 2.1.5

Multiply $2$ by $- 5$ .

$- 6 + 10 \sqrt{3} + 2 \sqrt{3} - 10$

Step 2.2

Subtract $10$ from $- 6$ .

$- 16 + 10 \sqrt{3} + 2 \sqrt{3}$

Step 2.3

Add $10 \sqrt{3}$ and $2 \sqrt{3}$ .

$- 16 + 12 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 16 + 12 \sqrt{3}$

Decimal Form:

$4.78460969 \dots$